Abstract
The mathematical property of one-dimensional steady solution for reverse smolder waves in the context of a model that permits both fuel-rich and fuel-lean has been studied using the method of analysis. Based on the equations and the boundary conditions some asymptotic properties of the solution at infinity are proved. It is shown that the value of oxygen or the mass of fuel (corresponding to the fuel-rich case and the fuel-lean case, respectively) tends to zero, and the temperature approaches to a fixed value. This is confirmed by other authors using large activation energy asymptotic methods.
Similar content being viewed by others
References
Dodd, A.B., Lautenberger, C., Fernandez-Pello, C. Computational modeling of smolder combustion and spontaneous transition to flaming. Combust. Flame, 159: 448–461 (2012)
Huang, X.Y., Rein, G. Smouldering combustion of peat in wildfires: Inverse modeling of the drying and the thermal and oxidative decomposition kinetics. Combust. Flame, 161(6): 1633–1644 (2014)
Kansa, E.J., Perlee, H.E., Chaiken, R.F. Mathematical model of wood pyrolysis including internal forced convection. Combust. Flame, 29: 311–324 (1977)
Kinbara, T., Endo, H., Sega, S. Downward propagation of smouldering combustion through solid materials. Proc. Combust. Ins., 11(1): 525–531 (1967)
Leisch, S.O., Kauffman, C.W., Sichel, M. Smouldering combustion in horizontal dust layers. Proc. Combust. Ins., 20(1): 1601–1610 (1985)
Lu, Z.B., Buckmaster, J., Chen, M., Massa, L. Instabilities of reverse smolder waves. Combust. Theory Model., 10(3): 515–534 (2006)
Lu, Z.B., Dong, Y. Instabilities of reverse smolder waves. Combust. Theory Model., 15(6): 795–815 (2011)
Ohlemiller, T.J. Modeling of smoldering combustion propagation. Prog. Energy Combust. Sci., 11: 277–310 (1985)
Ohlemiller, T.J., Bellan, J., Rogers, F. A model of smoldering combustion applied to flexible polyurethane foams. Combust. Flame, 36: 197–215 (1979)
Palmer, K.N. Smouldering combustion of dusts and fibrous materials. Combust. Flame, 1: 129–154 (1957)
Rein, G. Smouldering combustion phenomena in science and technology. Int. Rev. Chem. Eng., 1: 3–18 (2009)
Schult, D.A., Matkowsky, B.J., Volperb, V.A. Fernandez-Pello, A.C. Propagation and extinction of forced opposed flow smolder waves. Combust. Flame, 101: 471–490 (1995)
Yuan, F.P., Lu, Z.B. Structure and stability of non-adiabatic reverse smolder waves. Appl. Math. Mech.-Engl. Ed., 34(6): 657–668 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, Qs., Xu, Lx. A mathematical approach to the property of one-dimensional steady solution of reverse smolder waves. Acta Math. Appl. Sin. Engl. Ser. 33, 201–206 (2017). https://doi.org/10.1007/s10255-017-0651-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-017-0651-8